To be quite illiterate, not to know even his letters. Miege tells
us that hornbooks used to be called battledoors. The phrase
might therefore originally mean not to know the B of, from, or out of,
your hornbook. But its more general meaning is “not able to distinguish
one letter from another.”

“He knoweth not a B from a battledoore.” —Howell; English
Proverbs.

“Distinguish a B from a battledore.” —Dekker: Guls Hornebook.

I know B from a Bull's foot.

Similar to the proverb, “I know a hawk from a hernshaw.” (See
Hawk.) The bull's parted hoof somewhat resembles a B.

“There were members who scarcely knew B from a bull's foot.” —
Brackenbridge: Modern Chivalry.